Question

$3.7\text{g}$ of a gas at ${25}^{\circ }\text{C}$ occupies the same volume as $0.184\text{g}$ of hydrogen at ${17}^{\circ }C$ at the same pressure. What is the molecular mass of the gas (round off to the nearest integer)?

Answer 1

For hydrogen,
$w=0.184\text{g};T=17+273=290\text{K};M=2g/mol$
We know that,
$PV=\frac{w}{M}RT$
$PV=\frac{0.184}{2}\times R\times 290...\left(1\right)$
For the unknown gas,
$w=3.7\text{g};T=25+273=298\text{K};M=?$
$PV=\frac{3.7}{M}\times R\times 298...\left(2\right)$
Equating both the equations as P and V are the same,
$\frac{3.7}{M}\times R\times 298=\frac{0.184}{2}\times R\times 290$
or $M=\frac{3.7\times 298\times 2}{0.184\times 290}=41.33g/mol$